A few years ago, recreational mathematician, Vi Hart, declared October “Fexagon Month” in honor of Martin Gardner. Gardner, born October 21, 1914, wrote a monthly column on “recreational mathematics” for Scientific American from 1965 to 1981, and it all began with his article on hexaflexagons in the December 1956 issue.

A flexagon is a flat model that can be flexed or folded to reveal faces besides the two that were originally on the front and back. Watch these two videos from Vi Hart to learn more about the history of flexagons and how they work:

Flexagons are very cool to make and fun to play with. You can try making your own hexaflexagon from a strip of paper like Vi Hart shows in her video, or you can go to one of the tons of websites with colorful, printable templates that you can print out and fold according to the directions. Here are just a few:

Ada Lovelace is a international celebration aiming to raise the profile of women in science, technology, engineering and maths by encouraging people around the world to talk about the women whose work they admire

Ada Lovelace was an English mathematician and writer known for her work on Charles Babbage’s Analytical Engine, an early mechanical computer. She wrote what is recognized as the first algorithm intended to be processed by a machine, and, is often described as the world’s first computer programmer.

There are Ada Lovelace Day events worldwide. Check here to see if there is an event in your area.

Pascal’s triangle is a triangular array of the binomial coefficients. (But don’t worry, it isn’t important to understand binomial coefficients to do this activity.) Pascal’s Triangle is named after mathematician Blaise Pascal. Pascal did not invent this array, but he was the first to develop many of its uses and was the first to organize all the information about it together in a treatise.

To create your own Pascal’s Triangle, place a 1 in the first row (which contains only 1 number). In subsequent rows, each number is the sum of the two numbers above it, treating space outside the triangle as zero. Therefore, the next row, contains 0+1 or 1 and 1+0 or 1. The next row is 0+1, 1+1, and 1+0, as shown in the animation below.

The cool thing about Pascal’s Triangle is that there are a ton of patterns you can find. Here are just a few:

The first diagonal is all ones.

The second diagonal is the counting numbers.

The third diagonal is the triangular numbers.

The horizontal sums (adding across a row) are the powers of 2 (20=1, 21=2, 22=4, 23=8, 24=16, etc.).

Each row is a power of 11 (110=1, 111=11, 112=121, 113=1331, etc.).

And my favorite of all: if you color the odd numbers one color and the even numbers another color, you get a pattern that looks like the Sierpinski Triangle fractal.

Can you find any other patterns?

For more patterns, check out this cool page at Math is Fun. If you would like to challenge your kids or students to fill in Pascal’s Triangle and find some of the patterns, I have a worksheet here.